Stephen M. Pollock

Determination of the Optimal Process Mean and the Upper Limit for a Canning Problem

A method of determining the optimal process mean and upper fill weight limit for a canning process where the ingredients is expensive is presented. Underfilled (below a specified limit) and overfilled (above a controllable upper limit) cans are emptied ..

A Simple Model of Search for a Moving Target

A target moves between two regions in a Markovian fashion, the parameters of which are known to the searcher. Discrete amounts of search effort (“looks”) may be allocated to one region at a time. This paper gives equations that characterize (a) the minimum expected number of looks to detect the target, and (b) the maximum probability of detecting the target within a given number of looks. These are solved completely for special cases, and numerical approximate solutions are described for general cases.

Cost-optimal condition-monitoring for predictive maintenance of 2-phase systems

The deterioration processes of many industrial systems can be modeled in 2-phases. A 2-phase system begins its life in a new condition where it resides for a random amount of time before progressing to a worn condition where it resides for a random amount of time preceding system failure. If monitoring takes place while the system is in the worn condition, preventive maintenance is performed. This paper analyzes predictive maintenance policies for systems exhibiting 2-phase behavior, and presents cost-minimizing policies, as well as satisfying policies, to determine when monitoring should take place, and for allocating monitoring resources to multiple systems. The solution approach is based on decomposing the expected cost (per unit time) into 2 components: the expected cost due to maintenance actions, and the expected cost due to monitoring actions. This decomposition facilitates the construction of operating-characteristic curves that represent policy performance, and allows evaluation of the policy tradeoffs in many situations including those with constrained or unconstrained monitoring resources, multiple or single systems, and fixed or nonfixed monitoring intervals.

Cost savings due to variance reduction in a canning process

Abstract We investigate a canning problem (Golhar and Pollock [2]) to study the effect of a reduction in process variance on the production cost. Exact and approximate relationships are developed for cost reduction as a function of economic parameters when the fill is a normally distributed random variable and process settings are optimized.

Approximation analysis of open acyclic exponential queueing networks with blocking

An arbitrary configuration of an open queueing network with exponential service times and finite buffers is analyzed. We offer an iterative procedure for approximating the marginal occupancy probabilities for each queue of the system. The method decomposes the queueing network into individual queues and analyzes each in isolation using information from only its nearest neighbors. Based upon the SIMP approximation previously used for tandem queues, it replaces each servers service time with a clearance time, which includes blocking, and each servers arrival rate by an equivalent acceptance rate. The procedure is easy to implement and requires modest memory and computer time. Extensive numerical experiments, performed for various topologies, yield accurate results compared with those obtained by exact or simulation methods.

An application of Bayesian statistical methods to adaptive radiotherapy

In adaptive radiotherapy, measured patient-specific setup variations are used to modify the patient setup and treatment plan, potentially many times during the treatment course. To estimate the setup adjustments and re-plan the treatment, the measured data are usually processed using Kalman filtering or by computing running averages. We propose, as an alternative, the use of Bayesian statistical methods, which combine a population (prior) distribution of systematic and random setup errors with the measurements to determine a patient-specific (posterior) probability distribution. The posterior distribution can either be used directly in the re-planning of the treatment or in the generation of statistics needed for adjustments. Based on the assumption that day-to-day setup variations are independent and identically distributed Normal distributions, we can efficiently compute parameters of the posterior distribution from parameters of the prior distribution and statistics of the measurements. We illustrate a simple procedure to apply the method in practice to adaptive radiotherapy, allowing for multiple adjustments of treatment parameters during the course of treatment.

Approximations and Sensitivity in Multiobjective Resource Allocation

This paper addresses the modeling of resource allocation planning problems having uncertainties, multiple competing objectives, organizational constraints, and continuous decision variables. The application of multiobjective decision analysis leads to a nonlinear programming formulation in which the objective function is the expectation of a multiattribute utility function. If a set of independence conditions holds, this function can be decomposed into appropriately scaled sums and products of one-dimensional expected utility functions. Approximations that greatly simplify the data acquisition for, and the construction of, the one-dimensional expected utility functions are discussed. Sensitivity analyses indicate that optimal solutions to such models are robust with respect to changes in the required data, but may be seriously in error if certain popular, but overly simplified, forms for the objective function are assumed.

Artificial Inflation of a Delinquency Rate by a Selection Artifact

Cohorts of youths sentenced to a variety of correctional programs show substantial reductions in delinquent activity after leaving the programs compared to before sentencing. This paper develops models of delinquent activity and subsequent sentencing to a correctional program. We show how a population of youths, whose delinquent activity is represented by a stationary stochastic process, can be selected (using reasonable selection rules) to form a cohort which has an inflated rate of delinquent activity prior to selection. When the activity rate returns to its uninflated rate after the youths are released from the program, an apparent reduction results. Based on this analysis we conclude that the reductions noted in delinquent activity may be largely due to the way delinquents are selected for correction rather than to the effect of the programs.

A Bayesian Reliability Growth Model

A model is presented for the change (growth) in reliability of a system during a test program. Parameters of the model are assumed to be random variables with appropriate prior density functions. Expressions are then derived that enable estimates (in the form of expectations) and precision statements (in the form of variances) to be made of: 1) projected system reliability at time ? after the start of the test program, and 2) system reliability after the observation of failure data. Numerical examples are presented, and extension to multimode failures is indicated.

Approximate Analysis for the Merge Configuration of an Open Queueing Network with Blocking

Abstract A merge configuration of open queueing networks with exponential service times and finite buffers is analysed. We offer an iterative algorithm to approximate the steady-state probabilities for each queue of the system. The procedure decomposes the queueing network into individual queues and analyses each individual queue in isolation. An M/M/l/N or M/G/l/N model is used for the analysis of the merging queues; an M/M/l/N with state dependent arrival rates is used for the receiving queue. The approximation method is easy to implement, requires little memory, is computationally fast and yields very accurate results.